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Positive solutions of nonlinear problems involving the square root of the Laplacian
Cabré Vilagut, Xavier; Tan, Jinggang
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
We consider nonlinear elliptic problems involving a nonlocal operator: the square root of the Laplacian in a bounded domain with zero Dirichlet boundary conditions. For positive solutions to problems with power nonlinearities, we establish existence and regularity results, as well as a priori estimates of Gidas-Spruck type. In addition, among other results, we prove a symmetry theorem of Gidas-Ni-Nirenberg type.
Àrees temàtiques de la UPC::Matemàtiques i estadística
Fractional Laplacian
critical exponent
nonlinear mixed boundary problem
a priori estimates
nonlinear Liouville theorems
moving planes method
Teories no-lineals
Attribution-NonCommercial-NoDerivs 3.0 Spain
Article - Draft

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